# Hw05 - STAT 410 Homework#5(due Friday February 22 by 3:00...

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STAT 410 Spring 2008 Homework #5 (due Friday, February 22, by 3:00 p.m.) 1. Let X, Y, and Z be i.i.d. Uniform [ 0 , 1 ] random variables Find the probability distribution of W = X + Y + Z. That is, find ( ) w f W . Hint : If V = X + Y, we know the p.d.f. of V, f V ( v ) ( see Examples for 02/11/2008 ): f V ( v ) = v if 0 < v < 1, f V ( v ) = 2 – v if 1 < v < 2, f V ( v ) = 0 otherwise. Now use convolution formula to find the p.d.f. of W = V + Z. There will be 5 possible cases, 2 of them are "boring". 2. Suppose the size of largemouth bass in a particular lake is uniformly distributed over the interval 0 to 8 pounds. A fisherman catches (a random sample of) 5 fish. a) What is the probability that the smallest fish weighs less than 2 pounds? b) What is the probability that the largest fish weighs over 7 pounds? c) What is the probability that the largest fish weighs between 6 and 7 pounds?

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Hw05 - STAT 410 Homework#5(due Friday February 22 by 3:00...

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